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 The
movement of the planets has interested mankind for ages. Several
models, some quite complicated, involving for example
spheres nested within other spheres, have been set up to try to explain
this
movement, or to
predict future positions. One breakthrough came when Johannes Kepler,
building on the extensive observations of Tycho Brahe, in the sixteenth
century formulated his
laws of planetary motion. After decades of failed attempts to
describe this motion with various geometrical bodies, Kepler had
hit on the idea of using
ellipses. (He studied the orbit of the planet Mars.) It is therefore
remarkable that Newton could show, a few decades later, that the
elliptical movement is a mathematical consequence of
his own three laws of motion. (Newton's laws of motion are far more
general than statements about orbits of planets.)
In this project we will try to understand Newton's argument. One of
our sources will be a guest lecture to first year students, given
by physicist Richard Feynman. (As documented in the book "Feynman's Lost lecture: The motion of
planets around the sun.") In that lecture he used only elementary physics
and high school geometry. (And maybe also some ingenuity.) At some point, Feynman
had to abandon Newton's line of argument and devise his own. Likewise, in this project, we might need to make up our
own proof or two as well!
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